正态总体中线性可预测变量的Minimax预测

Minimax predictor of linear predictable variable in normal populations

在二次损失下研究了任意秩有限总体中线性可预测变量Ay的线性预测在一切预测类中的Minimax性.对于一般随机效应线性模型y=Xβ+ε,βε～NBα0,σ2UWW′V,这里X,B,U,V和W是已知矩阵,α∈Rk和σ2>0是未知参数,文中得到了Ay的惟一Minimax预测.

Under the condition of a quadratic loss,the minimax property of linear prediction function of a linear predictable variable Ay in the class of all the predictors is investigated.Considering the general random effect linear model y=Xβ+ε,βε~NBα0,σ~2UWW′V,where X,B,U,V and W are known matrices,and α∈R^k and σ~2>0 are parameters,the unique minimax predictor of Ay is obtained.